Improved Online Algorithm for Fractional Knapsack in the Random Order Model

Giliberti, Jeff; Karrenbauer, Andreas

doi:10.1007/978-3-030-92702-8_12

Cited by 3 publications

(3 citation statements)

References 28 publications

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“…To our knowledge, Karrenbauer and Kovalevskaya (2020) are the first to investigate the continuous knapsack problem in the random order model; they present a 9.37-competitive algorithm for the problem. The current state of the art is the 4.39-competitive algorithm proposed by Giliberti and Karrenbauer (2021). We contribute to the literature by studying an important variant of the online continuous knapsack problem and proposing an asymptotic 6.027-competitive algorithm.…”

Section: Contributions To the Literaturementioning

confidence: 99%

“…Our analysis and algorithm draw on the findings of Giliberti and Karrenbauer (2021) for the continuous knapsack problem and Albers et al (2021) for the 0-1 knapsack problem, both in the random order model. The CKP generalizes the continuous knapsack problem by considering concave piecewise-linear utility functions and the cardinality constraint, which significantly impacts our algorithm's analysis.…”

Section: Online Ckp In the Random Order Modelmentioning

confidence: 99%

“…Moreover, the arrival order is unknown, and one must make irrevocable decisions about picking an item before the next arrives (Marchetti-Spaccamela and Vercellis 1995). However, despite its important applications, the online continuous knapsack problem has received limited attention in the literature (Giliberti and Karrenbauer 2021).…”

Section: Introductionmentioning

confidence: 99%

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Cardinality-Constrained Continuous Knapsack Problem with Concave Piecewise-Linear Utilities

Bai¹,

Cardonha²

2023

Preprint

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We study an extension of the cardinality-constrained knapsack problem where each item has a concave piecewise-linear utility structure. Our main contributions are approximation algorithms for the problem and the investigation of an online version in the random order model. For the offline problem, we present a fully polynomial-time approximation scheme and show that it can be cast as the maximization of a submodular function with cardinality constraints; the latter result allows us to derive a greedy (1 − 1 e )approximation algorithm. For the online problem in the random order model, we present a 6.027-competitive algorithm. Finally, we investigate the empirical performance of the greedy and online algorithms in numerical experiments.

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Section: Contributions To the Literaturementioning

confidence: 99%

Section: Online Ckp In the Random Order Modelmentioning

confidence: 99%